A116719 Number of monocyclic skeletons with n carbon atoms and a ring size of 4.

1, 1, 4, 8, 24, 55, 147, 365, 954, 2431, 6327, 16369, 42743, 111595, 292849, 769805, 2030456, 5366844, 14222475, 37768154, 100510364, 267987501, 715847932, 1915406263, 5133382014, 13778469949, 37035674682, 99683747508, 268647638770, 724879674667, 1958151665752

Offset

4,3

Links

Andrew Howroyd, Table of n, a(n) for n = 4..200

Camden A. Parks and James B. Hendrickson, Enumeration of monocyclic and bicyclic carbon skeletons, J. Chem. Inf. Comput. Sci., vol. 31, 334-339 (1991).

Example

If n=5 then the number of monocyclic skeletons with ring size of four is 1.

Mathematica

G[n_] := Module[{g}, Do[g[x_] = 1 + x*(g[x]^3/6 + g[x^2]*g[x]/2 + g[x^3]/3) + O[x]^n // Normal, {n}]; g[x]];
T[n_, k_] := Module[{t = G[n], g}, t = x*((t^2 + (t /. x -> x^2))/2); g[e_] = (Normal[t + O[x]^Quotient[n, e]] /. x -> x^e) + O[x]^n // Normal; Coefficient[(Sum[EulerPhi[d]*g[d]^(k/d), {d, Divisors[k]}]/k + If[OddQ[ k], g[1]*g[2]^Quotient[k, 2], (g[1]^2 + g[2])*g[2]^(k/2-1)/2])/2, x, n]];
a[n_] := T[n, 4];
Table[a[n], {n, 4, 30}] (* Jean-François Alcover, Jul 03 2018, after Andrew Howroyd *)

Crossrefs

Column k=4 of A305059.

Cf. A063832.

Sequence in context: A115641 A153334 A332871 * A159612 A099176 A190156

Adjacent sequences: A116716 A116717 A116718 * A116720 A116721 A116722

Keyword

nonn

Author

Parthasarathy Nambi, Aug 13 2006

Extensions

More terms from N. J. A. Sloane, Aug 27 2006

a(5) corrected and terms a(26) and beyond from Andrew Howroyd, May 24 2018

Status

approved